Modulational instability

Bifurcation of gravity-capillary Stokes waves with constant vorticity
We construct Stokes waves for any values of the parameters, using variational methods.
T. Barbieri, M. Berti, A. Maspero, M. Mazzuchelli
PDF Code Project arXiv
First isola of modulational instability of Stokes waves in deep water
We prove high-frequency modulational instability of small-amplitude Stokes waves in deep water under longitudinal perturbations, providing the first isola of unstable eigenvalues branching off from i3/4.
M. Berti, A. Maspero, P. Ventura
PDF Code Project EMS Surv. Math. Sci
On higher order isolas of unstable Stokes waves
We prove asymptotic expansion when the depth goes to infinity of the function $\beta^{(p)}_1(h)$ for $p=2,3,4$.
M. Berti, L. Corsi, A. Maspero, P. Ventura
PDF Code Project arXiv